A Timeon Model of Quark and Lepton Mass Matrices

Abstract

It is proposed that $T$ violation in physics, as well as the masses of electron and $u, d$ quarks, arise from a pseudoscalar interaction with a new spin 0 field $\tau(x)$, odd in $P$ and $T$, but even in $C$. This interaction contains a factor $i\gamma_5$ in the quark and lepton Dirac algebra, so that the full Hamiltonian is $P$, $T$ conserving; but by spontaneous symmetry breaking, the new field $\tau(x)$ has a nonzero expectation value $<\tau>\neq 0$ that breaks $P$ and $T$ symmetry. Oscillations of $\tau(x)$ about its expectation value produce a new particle, the "timeon". The mass of timeon is expected to be high because of its flavor-changing properties. The main body of the paper is on the low energy phenomenology of the timeon model. As we shall show, for the quark system the model gives a compact 3-dimensional geometric picture consisting of two elliptic plates and one needle, which embodies the ten observables: six quark masses, three Eulerian angles $\theta_{12}, \theta_{23}, \theta_{31}$ and the Jarlskog invariant of the CKM matrix. For leptons, we assume that the neutrinos do not have a direct timeon interaction; therefore, the lowest neutrino mass is zero. The timeon interaction with charged leptons yields the observed nonzero electron mass, analogous to the up and down quark masses. Furthermore, the timeon model for leptons contains two fewer theoretical parameters than observables. Thus, there are two testable relations between the three angles $\theta_{12}, \theta_{23}, \theta_{31}$ and the Jarlskog invariant of the neutrino mapping matrix.